Characterisation of the Tri-Modal Discrete Sea Clutter Model
Summary (3 min read)
Introduction
- The study and analysis of sea clutter is important in many different applications such as oceanography, maritime surveillance and target classification.
- Models for the amplitude distribution of sea clutter are usually developed empirically from measurements of real data as it is not currently possible to accurately predict the PDF of sea clutter under different conditions using physical models of the sea surface.
- There has been a long development of PDF models used to fit both real aperture radar and synthetic aperture radar.
- In Section II, a number of key PDF models are described with details on how their parameters are estimated and the model fits assessed.
- Section IV then looks further at the texture estimates of the 3MD model over a wide parameter space.
II. AMPLITUDE DISTRIBUTION MODELS
- To understand the development of the compound distribution, consider a radar receiving in-phase and quadrature data from an external clutter source with its amplitude defined by Gaussian statistics with zero mean and variance, x.
- In addition, thermal noise from the radar will add a component σ2n which is included by offsetting the variance x.
- In target 2 detection analysis, the envelope of the received pulses is often converted to power (square law) and the clutter distribution becomes exponential.
- To include the texture component which modulates the speckle, the authors integrate over the speckle mean power, P (z) = ∫ ∞ 0 P (z|x)P (x)dx (2) where P (x) is the distribution of the texture component.
- While there are analytic solutions in many cases, when noise is included in the model, numerical integration must be used to evaluate the compound distribution.
B. Pareto model
- The Pareto model is described by only two parameters (shape and scale), yet can reasonably model the long tails present in sea-clutter distributions.
- It was first used for seaclutter modelling by Balleri et al. [4] and later by others at US Naval Research Laboratory (NRL) and DST Group [5]–[7].
- Similarly to the K+Rayleigh model, the distribution parameters can be estimated using method of moments, the 〈z log z〉 method or least squares minimisation.
- The 3MD model [10], [11] instead proposes the use of a discrete texture model that assumes the sea clutter consists of a finite number of distinct modes or scatterer types, I .
- In the original work, it was found that I = 3 modes were sufficient to model distributions from the spaceborne SAR imagery, hence the tri-modal in the name.
D. Error metrics
- To evaluate how well a model fits a set of observations, there are many statistical tests and measurement techniques in the literature including the mean squared error of the distribution model compared to the data [7], the chi-square and Kolmogorov-Smirnov tests and the Bhattacharyya distance [13].
- The first metric used in this paper is the Bhattacharyya distance (BD) which captures the similarity between the actual PDF, P (·) and the theoretical distribution, Q(·) DBD = − ln (∑ xk √ P (xk)Q(xk) ) (7) 3 where xk represents the data samples.
- The second metric is the threshold error which is determined by first calculating the CCDF for both the empirical data and the data fit.
- The threshold error is then the absolute difference between the two results at a fixed CCDF value.
- This view of the data is important due to its relationship with the threshold in a detection scheme used for distinguishing between targets and interference.
III. DATA SELECTION
- A. Ingara real beam data Ingara is a polarimetric radar system maintained and operated within the DST Group in Australia [14].
- During the ocean backscatter collections in 2004 and 2006, it was operated at X-band in a circular spotlight-mode where the aircraft flew a circular orbit in an anti-clockwise direction (as seen from above) around a nominated point of interest.
- An example of the data is shown in Fig. 1 for the downwind direction and 30◦ grazing.
- Table I shows the estimated parameters of the three models.
- The threshold errors which focus on the distribution tail, reveal that the K+Rayleigh and Pareto+noise models have a similar fitting error, while the 3MD model is significantly lower.
B. SETHI Synthetic Aperture Radar data
- In 2015, fully polarimetric SAR data was acquired off the French coast at both X- and Lbands simultaneously.
- Fig. 4. SETHI L-band SAR data in the upwind direction.
- To highlight common trends between the distributions, the K+Rayleigh shape estimates are shown in Fig.
- This matches where the K+Rayleigh shape value is low indicating the spikiest clutter.
B. SETHI data set
- The authors now investigate the 3MD parameters for the SETHI data sets, where the data is pooled into blocks of 0.1◦ grazing containing approximately 104−105 samples.
- Similarly to the Ingara data analysis, the authors observe that the third mode is required less for the VV polarisation, while the HH and HV polarisations nearly always require 3 modes, which is not the case for the Ingara dataset.
- This also confirms the need to take into account more complex backscattering mechanisms at higher frequencies [16], [17].
- The weighted texture parameters (ancn) are then studied in Figs. 9-10 over the grazing angle range 38◦-56◦.
- This is not unexpected as the data lies in the plateau scattering region where there is little variation with grazing angle.
V. CONCLUSION
- The 3MD model has been explored using data from the DST Group Ingara radar and the ONERA SETHI SAR.
- The 3MD model was shown to fit each data set extremely accurately over a wide range of geometries, two different frequency bands and both real aperture and synthetic aperture data.
- The model texture values were then studied to better understand their relationship to the underlying seaclutter characteristics.
- For the Ingara data, the spiky clutter region at low grazing angles in the HH polarisation nearly always required 3 modes with an even proportion spread between the first two modes (ancn ∼ 0.5).
- There were also a number of regions where the 3MD estimates were nearly all uni-modal, such as in the HV upwind direction and VV upwind and downwind directions.
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Citations
41 citations
28 citations
Cites background from "Characterisation of the Tri-Modal D..."
...Number of Modes Required for the 3MD Distribution In previous work, it has been reported that three modes are sufficient to accurately model amplitude distributions from spaceborne SAR data [17], airborne SETHI SAR data, and airborne INGARA real aperture sea clutter data [26]....
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...Although not shown here, this result matches where the KR shape value is lowest indicating the spikiest clutter [26]....
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...Among the 12 datasets (monostatic and bistatic), 7 need 2 or 3 modes (which is in agreement with [17] and [26]), but we find that 5 datasets need 4 or 5 modes....
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...In previous work, it has been reported that three modes are sufficient to accurately model amplitude distributions from spaceborne SAR data [17], airborne SETHI SAR data, and airborne INGARA real aperture sea clutter data [26]....
[...]
...Among the 12 datasets (monostatic and bistatic), 7 need 2 or 3 modes (which is in agreement with [17,26]), but we find that 5 datasets need 4 or 5 modes....
[...]
8 citations
Cites background from "Characterisation of the Tri-Modal D..."
...Since then, 3MD has been successfully applied to a very diverse set of airborne and space-based radar data and SAR imagery in different frequency bands and polarizations as well as EO/IR data, see [51]–[53]....
[...]
6 citations
Cites methods from "Characterisation of the Tri-Modal D..."
...The parameters may be estimated with a nonlinear LS fit to the data CCDF [9], [10], [19]....
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...Rosenberg and Angelliaume [9] applied the 3MD model to sea clutter data from real and synthetic aperture radars, finding that the model was able to represent the clutter statistics well in all cases....
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...In [9] and [10], the 3MD parameters were estimated with a nonlinear LS fit of the CCDF to the data....
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1 citations
Cites background or methods from "Characterisation of the Tri-Modal D..."
...3MD Distribution: Number of Modes It has previously been reported that I=3 modes are sufficient to accurately model amplitude distributions of high spatial resolution sea clutter data collected by spaceborne SAR sensors [10] as well as airborne RAR and SAR instruments [11]....
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...This paper builds on that work by studying the same NetRAD monostatic and bistatic dataset with two newer proposed sea clutter distributions from the literature: the K+Rayleigh [9] and the tri-modal (3MD) distributions [10]-[11]....
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...Among the 12 datasets (monostatic and bistatic), 7 need 2 or 3 modes (which is in agreement with [10] and [11]) but we find that 5 datasets need 4 or 5 modes....
[...]
References
42 citations
Additional excerpts
...SETHI SAR data used in this paper have been collected under the NAOMI (New Advanced Observation Method Integration) project, a common research program between TOTAL (the French petroleum company) and ONERA....
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...This is in contrast to the ONERA data which required 3 modes for nearly all fits to the HH and HV polarisations....
[...]
...For the ONERA data, it was found that less modes were required for the Lband data implying less complex backscattering mechanisms....
[...]
...In this paper, the 3MD model has been explored using data from the DST Group Ingara radar and the ONERA SETHI SAR....
[...]
...SETHI is an airborne remote sensing laboratory developed by ONERA [15] and operates as a pod-based system on a 4 Falcon 20 Dassault aircraft....
[...]
35 citations
"Characterisation of the Tri-Modal D..." refers background or methods in this paper
...The 3MD model [10], [11] instead proposes the use of a discrete texture model that assumes the sea clutter consists of a finite number of distinct modes or scatterer types, I ....
[...]
...The tri-modal discrete texture (3MD) model [10], [11] is another candidate which has demonstrated great potential for modelling synthetic aperture radar (SAR) sea-clutter and is unique in the way it models the sea clutter texture as a combination of discrete components....
[...]
35 citations
"Characterisation of the Tri-Modal D..." refers background or methods in this paper
...This model has been shown to fit both real and synthetic aperture radar data very accurately and over a wide range of geometries [9]....
[...]
...This contrast is important as the process of SAR image formation alters the radar backscatter with the SAR representation of ocean waves being different from that of real aperture radar [9]....
[...]
12 citations
"Characterisation of the Tri-Modal D..." refers methods in this paper
...To evaluate how well a model fits a set of observations, there are many statistical tests and measurement techniques in the literature including the mean squared error of the distribution model compared to the data [7], the chi-square and Kolmogorov-Smirnov tests and the Bhattacharyya distance [13]....
[...]
10 citations
"Characterisation of the Tri-Modal D..." refers background in this paper
...This also confirms the need to take into account more complex backscattering mechanisms at higher frequencies [16], [17]....
[...]
Related Papers (5)
Frequently Asked Questions (16)
Q2. What is the consequence of the discretisation of the texture?
One of the consequences of this discretisation is that spatial and longtime correlation cannot be modelled as part of the texture, and hence the model is less suitable for clutter simulation.
Q3. What is the common PDF model for sea clutter?
The most commonly used PDF model for sea-clutter in both real and synthetic aperture radar is the K-distribution, or K+noise when thermal noise is included.
Q4. What is the inverse gamma distribution of the texture?
For the Pareto distribution, the texture has an inverse gamma distributionP (x) = caΓ(a) x−a−1 exp [−c/x] , a > 1, c > 0 (4)where a is the shape and c = σ2c (a− 1) is the scale.
Q5. What is the common method to improve the detection performance of a radar?
For a frequency agile or scanning radar with sufficient time between looks, a common method to improve the detection performance is to sum a number of looks.
Q6. What is the distribution of the texture component?
To include the texture component which modulates the speckle, the authors integrate over the speckle mean power,P (z) = ∫ ∞ 0 P (z|x)P (x)dx (2)where P (x) is the distribution of the texture component.
Q7. What was the polarimetric radar used during the ocean backscatter collection in 2004?
During the ocean backscatter collections in 2004 and 2006, it was operated at X-band in a circular spotlight-mode where the aircraft flew a circular orbit in an anti-clockwise direction (as seen from above) around a nominated point of interest.
Q8. What is the gamma distribution for the texture component?
The K+Rayleigh model uses a gamma distribution for the texture,P (xr|νr, br) = bνrrΓ(νr) xνr−1r exp [−brxr] , 0 ≤ xr ≤ ∞ (3)where νr is the shape and br = νr/σ2c is the scale with the mean clutter power, σ2c .
Q9. What was the first use of the Pareto model?
It was first used for seaclutter modelling by Balleri et al. [4] and later by others atUS Naval Research Laboratory (NRL) and DST Group [5]–[7].
Q10. How is the inverse gamma distribution calculated?
To calculate the compound distribution in (2), the integration is then performed with the modified speckle mean level, xr instead of the total speckle x.
Q11. How can the authors estimate the distribution parameters of the sea clutter?
Similarly to the K+Rayleigh model, the distribution parameters can be estimated using method of moments, the 〈z log z〉 method or least squares minimisation.
Q12. What is the probability of infinite texture values?
The compound models in the literature all assume a continuous texture distribution function which suggests a small probability of infinite texture values.
Q13. What is the polarimetric range resolution of the SAR imagery?
The SAR imagery has range resolutions of 0.5 m and 1.0 m for the X and L-bands respectively, and the imaged area is processed with an azimuth (alongtrack) resolution equal to the range resolution.
Q14. What are the three models fitted to the data?
The K+Rayleigh, Pareto+noise and 3MD models have been fitted to the data with the model parameters shown in Tables III and IV for the X-band and L-band data sets.
Q15. What are the parameters used to estimate the long tails in the Pareto model?
The Pareto model is described by only two parameters (shape and scale), yet can reasonably model the long tails present in sea-clutter distributions.
Q16. What is the difference between the Ingara and HH data sets?
Similarly to the Ingara data analysis, the authors observe that the third mode is required less for the VV polarisation, while the HH and HV polarisations nearly always require 3 modes, which is not the case for the Ingara dataset.